A reconstruction method of a three-dimensional model of a vane pump based on an STL file

Abstract

The application provides a reconstruction method of a vane pump three-dimensional model based on an STL file, and specifically comprises the following steps: STL model data reconstruction of the vane pump based on a half-edge data structure; feature edge extraction of the STL model of the vane pump based on geometry preservation; sub-region division of the STL model of the vane pump based on an angle limit; STL model re-triangulation of the vane pump based on a RAR algorithm, including the following steps: constructing four operation operators; constructing constraint conditions of the operation operators based on the idea of geometry feature preservation, so as to preserve the geometry features of the vane pump model; determining a quality measurement index, so as to iteratively optimize the local vane pump STL model, and finally completing the model reconstruction. The application starts from the vane pump STL model, realizes the reconstruction of the vane pump STL model under the condition that the overall structure of the vane pump STL model is complete, and improves the quality of the triangular facets of the vane pump STL model.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of fluid machinery design, in particular to a three-dimensional model reconstruction method. BACKGROUND

[0002] The blade pump CAD model designed by CAD software usually needs to be manually processed for broken surface before meshing, while converting it into STL file format can avoid this operation. STL file is a file format using discretization representation, which can describe the surface of a three-dimensional model through a set of triangular facets, shielding the differences of different CAD systems. However, the blade pump STL model directly exported by CAD software is usually of poor quality, and if directly meshed, it will seriously affect the quality of the generated mesh after meshing. SUMMARY

[0003] Therefore, the application provides a blade pump three-dimensional model reconstruction method based on STL file. The application starts from the blade pump STL model, realizes the reconstruction of the blade pump STL model under the condition of meeting the overall structure integrity of the blade pump STL model, improves the triangular facet quality of the blade pump STL model, and establishes a blade pump STL model reconstruction method.

[0004] The application realizes the three-dimensional reconstruction of the blade pump STL model based on half-edge data structure and RAR algorithm.

[0005] The method comprises the following steps:

[0006] a: blade pump STL model data reconstruction based on half-edge data structure

[0007] STL (Stereolithography) model is a file format used to describe the surface of a three-dimensional object, which is composed of a series of triangular facets, each of which defines a part of the object surface. In the three-dimensional model of the blade pump, it usually contains complex geometric shapes, which are approximated and represented by triangular facets in the STL model. In addition, the STL model does not store the connection information between nodes, edges and triangular facets in the mesh, and each element is independent of each other without explicit topology structure. When reconstructing the blade pump STL model, the STL model needs to be converted into a data structure more suitable for mesh processing algorithm to reconstruct the topology.

[0008] The data reconstruction refers to creating a face object F for each triangular facet in the blade pump STL file. The face object F includes three vertices {V1, V2, V3} of the corresponding triangular facet, and three half-edge objects are established by the three vertices, which are V1V2, V2V3 and V3V1. Wherein V1V2 represents the direction of the half-edge from V1 to V2;

[0009] b: Feature edge extraction of blade pump STL model based on geometric retention

[0010] The STL model also contains some feature edges with significant geometric features, such as sharp edges or corners, which need to be identified and retained during data reconstruction to ensure the accuracy and integrity of the model. To ensure that the reconstructed blade pump STL model retains the key features of the original model, the key geometric feature edges need to be identified and extracted from the original blade pump STL model first.

[0011] In step b, the feature edge extraction step is as follows:

[0012] (1) According to the given normal angle threshold α of the blade pump specific speed, the normal angle threshold α of the blade pump specific speed is 50° for low specific speed (specific speed n s ≤80), 55° for medium specific speed (80<n s ≤220), and 60° for high specific speed (n s >220).

[0013] (2) Traverse all edges of the original blade pump STL model, and find the two triangular patches connected by each edge using topological data. Measure the included angle γ between the normal vectors of the two patches, then calculate the included angle β between the two patches, β is the complementary angle of γ. If β is greater than α, then the edge E is determined as a feature edge, and the feature edge is retained in the subsequent operation to maintain the geometric accuracy and details of the model, so that the reconstructed model is closer to the original design.

[0014] c: Sub-region division of blade pump STL model based on angle restriction

[0015] In the blade pump STL model, there may be continuous smooth structures such as cylindrical surfaces and various curved surfaces, which need to be represented by a series of continuous smooth triangular patches, but the edges of these smooth structures are usually not automatically identified as feature edges. Restricting the angle between the normal vectors of the triangular patches of the blade pump STL model and dividing the sub-regions can avoid the entire continuous smooth structure being mistakenly identified as a single sub-region. Independent sub-regions refer to regions with significantly different geometric features in the model, which are divided according to the difference in normal vector angle, so that each region can be handled more carefully. This division can ensure that different geometric features are not confused during data reconstruction, thereby improving the accuracy and integrity of the model. The specific steps are as follows:

[0016] (1) Arbitrarily select a triangular patch as the starting point of a separate sub-region, and expand outward along the three edges of the starting triangular patch to include adjacent triangular patches in the same sub-region.

[0017] (2) The expansion operation is performed cyclically until the included angle γ of the normal vectors of a pair of adjacent triangular facets is greater than α, and the expansion is stopped at this time, and the region formed at this time is an independent sub-region.

[0018] d: RAR algorithm-based STL model of blade pump re-triangulation

[0019] By constructing four kinds of operation operators to move and adjust the vertices of the original blade pump STL model locally, the original blade pump STL model is reconstructed, and the edge length of the triangular facet is taken as the quality measurement index, and the local blade pump STL model is iteratively optimized until the curvature field weighted edge length is approximately consistent, thereby achieving the purpose of reconstruction.

[0020] The main operation operators in step d are as follows:

[0021] (1) Define four reconstruction geometry algorithms, specifically vertex movement, edge flip, edge collapse, and edge cut.

[0022] Vertex movement: by moving the vertices of the triangular facet to the weighted area average position formed by all triangular facets, the shape and topological structure of the model are adjusted, and vertex movement is used to eliminate small fluctuations and irregularities on the model surface, making the surface smoother and more continuous.

[0023] Edge flip: by adjusting the edges of adjacent triangles, the connection relationship of the triangles is changed. Specifically, two triangular facets with adjacent edges are constructed into a quadrilateral, and another diagonal line is connected to form two new triangular facets. Edge flip can reduce the occurrence of thin triangles in the STL model, making the distribution of triangular facets on the curved surface more natural and uniform, thereby improving the surface quality.

[0024] Edge collapse: by merging two adjacent vertices into one vertex, redundant edges are eliminated. Specifically, two vertices of a triangular facet are merged into one point, and the two adjacent triangular facets are eliminated. Edge collapse simplifies the grid structure by reducing the number of vertices and edges, thereby reducing the complexity of the model.

[0025] Edge cut: this operator is used to insert new vertices and edges into the STL model, thereby increasing the fineness of the STL model. Edge cut can significantly increase the resolution of the model and improve the smoothness of the model surface. By increasing more vertices and edges, the model surface can better approximate a continuous curved surface, thereby reducing surface irregularity and roughness.

[0026] (2) Determine the target edge length as the quality measurement index

[0027] In the process of STL model reconstruction, the target edge length as a quality metric indicator can not only help to control the density and accuracy of the triangular facets of the model, but also unify the structure of the entire model. Setting an appropriate target edge length helps to ensure that the model has a suitable grid resolution in different areas, thereby maintaining sufficient accuracy in geometric expression. Therefore, the edge length of the triangular facet is used as a quality metric indicator to control the degree of re-triangulation of the triangular facet. If the edge lies on a plane, the target edge length is the average triangular facet edge length of the input STL model; if the edge lies on a quadratic surface, the target edge length is determined by the following formula:

[0028]

[0029] In the formula, ε is the error, which is taken as 1% of the average triangular facet edge length of the blade pump STL model; R is the radius of the inscribed circle of the circular arc corresponding to the edge, which can be determined by the parameter definition of the curved surface.

[0030] If the edge lies on a NURBS surface, the target edge length is determined by the following formula:

[0031]

[0032] In the formula, k is the maximum absolute curvature on the edge.

[0033] (3) Construction of constraints

[0034] For the above four reconstruction geometry algorithms, the following constraints are constructed based on the idea of geometric feature preservation to maintain the geometric features of the blade pump model.

[0035] Constraint one: for vertex movement, triangular inversion and degeneration judgment are performed on the adjacent triangular facets of the moved triangular facet, and if inversion and degeneration occur, the vertex movement operation is not performed.

[0036] Constraint two: for edge flipping process, the projection of the constructed quadrilateral on the tangent plane is judged, and the flipping operation is only performed when the projection is not a convex polygon. After flipping, the difference between the midpoint of the diagonal of the quadrilateral before and after flipping and the projection distance to the original STL model is checked, and if it is greater than the set distance, the flipping operation is restored.

[0037] Constraint three: for edge collapse process, it is judged whether the normal angle of the triangular facet before and after collapse exceeds 90°, and if it exceeds 90°, the edge collapse operation is not performed.

[0038] Constraint four: for edge cutting process, the edge length of the triangular facet before and after cutting is judged, and if it is less than the set distance, the edge cutting operation is not performed.

[0039] (4) Geometric reconstruction

[0040] Input: initial vane pump STL model, average edge length L, error epsilon.

[0041] Step one: traverse all points on the feature edge, if the point is on the boundary, the target edge length L m is calculated by formula (1); otherwise, determine the surface type, if it is a plane, then L m =L; if it is a quadratic surface, determine the target edge length L m according to the surface parameters by formula (1); if it is a NURBS surface, the target edge length L m is determined by formula (2).

[0042] Step two: traverse each edge of the triangular facet, if the edge length is greater than the target edge length 0.75L m , perform edge cutting operation.

[0043] Step three: traverse each edge of the triangular facet, if the edge length is less than the target edge length 0.2L m and is not a feature edge, then perform edge flipping operation.

[0044] Step four: traverse each edge of the triangular facet, if the normal angle of the two triangular facets on both sides of the edge is less than 30°, and the sum of the two angles opposite to the edge is greater than 180°, then perform edge collapse.

[0045] Step five: perform vertex moving operation on all non-boundary points.

[0046] Step six: repeat steps one to four until all edge lengths meet the target edge length requirements.

[0047] Output: reconstructed vane pump STL model.

[0048] Beneficial effects

[0049] 1. The method can greatly improve the quality of triangular facets divided by the vane pump three-dimensional model, has the advantages of accurate identification results, high efficiency, good repair effect, etc., and can greatly improve the quality of the vane pump three-dimensional model.

[0050] 2. The STL (Stereolithography) model is a file format for describing the surface of a three-dimensional object, and each element is independent of each other without explicit topology. The application first reconstructs the data and converts the STL model into a data structure more suitable for grid processing algorithm, which is beneficial to subsequent topology reconstruction.

[0051] 3. The application extracts feature edges, which is beneficial to maintain the geometric precision and details of the model, so that the reconstructed model is closer to the original design.

[0052] 4、The present application divides the areas with significantly different geometric characteristics according to the difference of the normal vector angle, so as to process each area more carefully. This division can ensure that the areas with different geometric characteristics are not confused in the data reconstruction process, thereby improving the accuracy and integrity of the model.

[0053] 5、In the STL model reconstruction process of the present application, determining the target edge length as a quality measurement index can not only help control the density and accuracy of the triangular facets of the model, but also unify the structure of the entire model. Setting an appropriate target edge length helps ensure that the model has appropriate grid resolution in different areas, thereby maintaining sufficient accuracy in geometric expression. BRIEF DESCRIPTION OF DRAWINGS

[0054] Figure 1 is a schematic diagram of half-edge data structure.

[0055] Figure 2a is a schematic diagram of vertex moving operator;

[0056] Figure 2b is a schematic diagram of edge flipping;

[0057] Figure 2c is a schematic diagram of edge collapse operator;

[0058] Figure 2d is a schematic diagram of edge cut operator;

[0059] Figure 3 is a flowchart of re-triangulation;

[0060] Figure 4 is the feature edge identification result of the embodiment;

[0061] Figure 5 is the sub-area division result;

[0062] Figure 6 is the STL model before reconstruction of the embodiment.

[0063] Figure 7 is the STL model after reconstruction of the embodiment.

[0064] Figure 8 Flowchart of 3D model reconstruction of vane pump DETAILED DESCRIPTION

[0065] The embodiments of the present application will be described in detail below with reference to the accompanying drawings. The present embodiments are implemented on the premise of the inventive technical solution, and detailed implementation methods and specific implementation processes are given, but the protection scope of the present application is not limited to the following embodiments. The present application is a method for reconstructing STL model of vane pump based on CAD platform.

[0066] Embodiment:

[0067] Take a blade pump with a specific speed of 118 as an example, its main geometric parameters are: impeller outlet width b2 = 30 mm, impeller outlet diameter D2 = 315 mm, base circle diameter D3 = 342, and inlet width b3 = 60.

[0068] Step one: STL model data reconstruction of blade pump based on half-edge data structure

[0069] For the embodiment, the half-edge data structure is established, and the steps are as follows:

[0070] For each triangular facet in the embodiment, a face object F is created. The face object F includes three vertices {V1, V2, V3} of the corresponding triangular facet, and three half-edge objects are established by the three vertices, which are V1V2, V2V3, and V3V1. Wherein V1V2 represents the direction of the half-edge from V1 to V2.

[0071] The specific steps of the data reconstruction are as follows:

[0072] (1) According to the triangular facet data of the blade pump STL model, a vertex table, a half-edge table and a face table are established;

[0073] (2) Process each triangular facet in the blade pump STL file, create a face object F for it, and record the vertex coordinates of the triangular facet; if a vertex already exists in the vertex table, the index of the vertex is directly used; otherwise, mark the three vertices as {V1, V2, V3}, and create the corresponding vertex object and store it in the vertex table;

[0074] (3) Three half-edge objects are established from the three vertices in (2), which are V1V2, V2V3, and V3V1. Wherein V1V2 represents the direction of the half-edge from V1 to V2.

[0075] (4) Associate the three half-edges with the face object F, and check and record the half-edges emitted by each vertex. For example, if the vertex V1 has not been associated with any emitted half-edge, record the half-edge V1V2 emitted from V1, set the next half-edge as V2V3, and set the face to which it belongs as face F.

[0076] (5) Traverse all the triangular facets in the blade pump STL file and repeat (2) to (4).

[0077] (6) Traverse the half-edge table, check each half-edge V1V2. If there is a symmetric half-edge V2V1, set the symmetric half-edge of V1V2 as V2V1.

[0078] Step two: feature edge extraction of blade pump STL model based on geometric preservation

[0079] The specific steps are as follows:

[0080] (1) According to the blade pump normal angle threshold a given by the specific speed, the low specific speed (specific speed n s ≤80) blade pump a is 50°, the medium specific speed (80<n s ≤220) blade pump is 55°, and the high specific speed (n s >220) blade pump a is 60°.

[0081] (2) Traverse all edges of the original blade pump STL model, and find two triangular facets connected by each edge using topological data. Measure the included angle γ between the normal vectors of the two facets, then calculate the included angle β between the two facets, β is the complementary angle of γ. If β is greater than a, then the edge E is determined as a feature edge, and the feature edge is retained in subsequent operations.

[0082] In this embodiment, the medium specific speed blade pump normal angle threshold a is 55°. The feature edge schematic diagram is as Figure 4 shown.

[0083] Step three: blade pump STL model sub-region division based on the normal angle restriction

[0084] The specific steps are as follows:

[0085] (1) Arbitrarily select a triangular facet as the starting point of a separate sub-region, and expand outward along the three edges of the starting triangular facet to include adjacent triangular facets in the same sub-region.

[0086] (2) Perform the expansion operation in a loop until the normal vector included angle γ of a pair of adjacent triangular facets is greater than a, and then stop the expansion. At this time, the region formed is an independent sub-region.

[0087] In this embodiment, the threshold is 55°, and the embodiment division schematic diagram is as Figure 5 shown.

[0088] Step four: blade pump STL model re-triangulation based on the RAR algorithm

[0089] The specific construction geometry algorithm is as follows:

[0090] Vertex movement: adjust the shape and topological structure of the model as a whole by moving the triangular facets locally. Specifically, move each vertex to the area-weighted average position of the center of all triangles formed by the point.

[0091] Edge flipping: change the connection relationship of the triangular facets by adjusting the edges of adjacent triangular facets. Specifically, construct a quadrilateral with two triangular facets that have adjacent edges, and reconnect the other diagonal to form two new triangular facets.

[0092] Edge collapse: the redundant edges are eliminated by merging two adjacent vertices into one vertex. Specifically, two vertices of an edge of a triangle are merged into one vertex, and the two adjacent triangles are eliminated.

[0093] Edge split: this operator is used to insert new vertices and edges in the STL model, thereby increasing the fineness of the STL model.

[0094] The specific reconstruction steps are as follows:

[0095] (1) Determine the quality metric

[0096] The quality metric is determined as the edge length of the triangle to control the degree of re-triangulation of the triangle. The target edge length is calculated in units of edges. First, the type of the surface where the triangle is located is determined. If the edge is located on a plane, the target edge length is the average triangle edge length of the input STL model. If the edge is located on a quadric surface, it is determined by the following formula:

[0097]

[0098] where ε is the error, which can be taken as 1% of the average triangle edge length of the blade pump STL model; R is the radius of the inscribed circle of the corresponding circular arc, which can be determined by the parameter definition of the surface.

[0099] If the edge is located on a NURBS surface, it is determined by the following formula:

[0100]

[0101] where k is the maximum absolute curvature on the edge.

[0102] (2) Build constraints

[0103] For the above four geometric algorithms, the following constraints are constructed based on the idea of geometric feature preservation to preserve the geometric features of the blade pump model.

[0104] Constraint one: for vertex movement, the adjacent triangles of the moved triangle are triangle-inverted and degenerate-judged. If inversion and degeneration occur, the vertex movement operation is not performed.

[0105] Constraint two: for edge flipping, the projection of the constructed quadrilateral on the tangent plane is judged. The flipping operation is only performed when the projection is not a convex polygon. After flipping, the difference between the midpoint of the diagonal of the quadrilateral and the projection distance to the original STL model is checked. If the difference is greater than the set distance, the flipping operation is restored.

[0106] Constraint three: for edge collapse, it is judged whether the normal angle of the triangle before and after collapse exceeds 90°. If it exceeds 90°, the edge collapse operation is not performed.

[0107] Constraint four: for edge cutting process, judge the length of edge before and after cutting, if less than the set distance, then do not perform edge cutting operation.

[0108] (3) Geometry reconstruction

[0109] Input: initial example, average edge length L, error ε.

[0110] Step one: traverse all points on the feature edge, if the point is on the boundary, calculate the target edge length Lm by formula (1) and multiply the corresponding coefficient; otherwise, judge the surface type, if it is a plane, then L m =L; if it is a quadratic surface, determine the target edge length L m according to the surface parameters by formula (1); if it is a NURBS surface, determine the target edge length L m by formula (2).

[0111] Step two: traverse each edge of the triangular patch, if the edge length is greater than the target edge length 0.75L m , perform edge cutting operation.

[0112] Step three: traverse each edge of the triangular patch, if the edge length is less than the target edge length 0.2L m and is not a feature edge, then perform edge flipping operation.

[0113] Step four: traverse each edge of the triangular patch, if the normal angle of the two triangular patches on both sides of the edge is less than 30°, and the sum of the two angles opposite to the edge is greater than 180°, then perform edge collapse.

[0114] Step five: perform vertex moving operation on all non-boundary points.

[0115] Step six: repeat steps one to four until all edge lengths meet the target edge length requirement.

[0116] Output: reconstructed example.

[0117] The comparison chart of the example before and after reconstruction is shown in Figure 6 , Figure 7 .

Claims

1. A method for reconstructing a 3D model of a vane pump based on an STL file, characterized in that... It includes the following specific steps: a: Data reconstruction of the STL model of a vane pump based on a half-side data structure; b: Feature edge extraction of the STL model of the vane pump based on geometry preservation; wherein, based on the specific speed of the vane pump, the normal angle threshold α is given, and the angle β between the two facets is calculated. If β is greater than α, then the edge E connecting the two facets is determined to be a feature edge. c: Sub-region partitioning of the vane pump STL model based on included angle constraints; wherein, the included angle refers to the included angle γ between the normal vectors of adjacent triangular facets; d: Retriangulation of the STL model of the vane pump based on the RAR algorithm includes: constructing four types of operation operators; constructing constraint conditions for the operation operators based on the idea of ​​geometric feature preservation to preserve the geometric features of the vane pump model; determining a quality metric index to perform iterative optimization of the local part of the vane pump STL model, and finally completing the model reconstruction; wherein, the quality metric index is determined to be the side length of the triangular facet to control the degree of retriangulation of the triangular facet.

2. The method for reconstructing a three-dimensional model of a vane pump based on an STL file according to claim 1, characterized in that: The data reconstruction refers to creating a face object F for each triangular face in the vane pump STL file. The face facing F includes the three vertices {V1, V2, V3} of the corresponding triangular face, and three half-side objects are created from the three vertices, namely V1V2, V2V3, and V3V1; where V1V2 indicates that the direction of the half-side is from V1 to V2.

3. The method for reconstructing a three-dimensional model of a vane pump based on an STL file according to claim 1, characterized in that: The feature edge extraction process is as follows: (1) The normal angle threshold α is given according to the specific speed of the vane pump. Specifically: under low specific speed, the normal angle threshold α of the vane pump is 50°; under medium specific speed, the normal angle threshold of the vane pump is 55°. At high specific speeds, the threshold normal angle α for the vane pump is 60°. (2) Traverse all edges of the STL model of the vane pump and use topological data to find the two triangular faces connected by each edge; measure the angle γ between the normal vectors of the two faces, and then calculate the angle β between the two faces. β is the complementary angle of γ. If β is greater than α, then the edge E is determined to be a feature edge.

4. The method for reconstructing a three-dimensional model of a vane pump based on an STL file according to claim 1, characterized in that: The sub-region division specifically includes: (1) Select a triangular facet as the starting point of a specific sub-region. Starting from this starting triangular facet, expand outward along its three sides to include adjacent triangular facets into the same sub-region. (2) Repeat the expansion operation until the angle γ between the normal vectors of a pair of adjacent triangular facets is greater than α, then stop the expansion. At this time, the region formed is an independent sub-region.

5. The method for reconstructing a three-dimensional model of a vane pump based on an STL file according to any one of claims 1-4, characterized in that: The four operation operators are vertex movement, edge flipping, edge collapse, and edge cutting.

6. The method for reconstructing a three-dimensional model of a vane pump based on an STL file according to claim 5, characterized in that: The constraints include, Constraint 1: For vertex movement, perform triangle inversion and degradation checks on the adjacent faces of the moved triangle. If inversion or degradation occurs, the vertex movement operation is not performed. Constraint 2: For the edge flipping process, the projection of the constructed quadrilateral onto the tangent plane is judged, and the flipping operation is only performed when its projection is not a convex polygon; after the flipping is completed, the difference between the midpoint of the diagonal of the quadrilateral before and after the flipping and the projection distance to the original STL model is checked. If it is greater than the set distance, the flipping operation is restored. Constraint 3: For the edge collapse process, determine whether the included angle between the normals of the two triangular facets before and after the collapse exceeds 90°. If it exceeds 90°, the edge collapse operation will not be performed. Constraint 4: For the edge cutting process, determine the edge length before and after cutting. If it is less than the set distance, then the edge cutting operation will not be performed.

7. The method for reconstructing a three-dimensional model of a vane pump based on an STL file according to claim 6, characterized in that: The target side length is calculated in units of sides. First, the type of surface on which the triangular facet is located is determined. If the edge lies on a plane, the target edge length is the average triangle edge length of the input STL model; If the edge lies on a quadratic surface, it is determined by the following formula: In the formula, ε is the error; R is the radius of the inscribed circle of the arc corresponding to the edge, which is determined by the parameter definition of the surface. If the edge lies on a NURBS surface, it is determined by the following formula: In the formula, k is the maximum absolute curvature on the edge.

8. The method for reconstructing a three-dimensional model of a vane pump based on an STL file according to claim 7, characterized in that: The retriangulation of the vane pump STL model based on the RAR algorithm specifically includes: Input: Initial STL model of a vane pump, average side length L, error ε; Step 1: Traverse all points on the feature edge. If the point is located on the boundary, calculate the target edge length L using equation (1). m Calculate; otherwise, determine the surface type. If it is planar, then L m =L; if it is a quadratic surface, then the target side length L is determined by equation (1) based on the surface parameters. m If it is a NURBS surface, then the target side length L m Determined by equation (2); Step 2: Traverse each edge of the triangular facet. If the edge length is greater than the target edge length by 0.75L... m Perform edge cutting operation; Step 3: Traverse each edge of the triangular facet. If the edge length is less than the target edge length by 0.2L... m If the edge is not a feature edge, then perform an edge flipping operation; Step 4: Traverse each edge of the triangular facet. If the included angle between the normals of the two triangular facets opposite the edge is less than 30° and the sum of the two angles opposite the edge is greater than 180°, then perform edge collapse. Step 5: Perform vertex movement operations on all non-boundary points; Step Six: Repeat steps one through five until all side lengths meet the target side length requirements; Output: The reconstructed STL model of the vane pump.

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